A wide range of flow phenomena in everyday life can be modelled accurately using classical continuum theory: the Navier-Stokes equations with associated no-slip conditions. However, oscillatory flows generated by nanoscale ...

We investigate a combinatorial analogue of the Ricci curvature flow for 3-dimensional hyperbolic cone structures, obtained by gluing together hyperbolic ideal tetrahedra. Our aim is to find a hyperbolic structure for ...

We introduce the geometric $\delta$-minimum bottleneck spanning tree problem ($\delta$-MBST), which is the problem of finding a spanning tree for a set of points in a geometric space (e.g., the Euclidean plane) such that ...

Differentiated instruction has been shown to be effective in improving student learning outcomes; however, the resulting work load can be difficult for teachers to manage. A teaching package known as the NRP (Number Resource ...

This thesis addresses four problems in continuous and discrete optimisation. The first problem is about using column generation – an advanced technique in mixed integer programming – to design schedules for students in the ...

We consider incomplete data problems in two different complex data contexts: group testing data and functional data. In the group testing data context, we consider estimating the conditional prevalence of a disease from ...

At any one time, more than 160 million children worldwide are infected with skin sores. In remote Aboriginal Australian communities, prevalence is as high as 40%. Skin sores infected with Group A Streptococcus (GAS) can ...

In this thesis, we use extreme value theory to fit statistical models to observations of Australian daily rainfall extremes. We build upon the existing literature by challenging the basic assumptions of these models when ...

In this thesis we consider a number of enumerative combinatorial problems. We solve the problems of enumerating Eulerian orientations by edges and quartic Eulerian orientations counted by vertices. We also find and prove ...

Fluid flows at micro- and nanometre length scales are governed by physical processes that are quite different to their macroscale counterparts. When these flows interact with suspended solid particles, a rich array of ...